Motorcycle Repair: 1984 Harley FLHTC Dresser, harley flhtc, speedo cable

Question
Have wanted one for 30 years. Anyway this what I was told it's a 1984 Harley FLHTC Dresser Vin # 1HD1DDL22EY700185. Has a new battery they told me.. #1 it's very hand cranking. I push the the button ( cold or warm) and it get's one revolution and stops. I let go not to burn out the starter. Some times it sound like it's kicking back and spits out the carb? It will start to crank over and then start, but this may have to be done three or more times. #2 the end of the speedo cable fell out of the front wheel. I thought it lost a clip and could be put back in, but I don't see anything inside there where the square cable should go into and how would it stay in there? ( lost parts?) #3 when I shift from 3rd to 4th sometimes it's like it's in neutral and I have to do it again. It does it down shifting also. Last I see it has a cover on the chain, when do I have to lube the chain? Thank You Richard

Answer
Even though you were told it has a new battery, you need to get it load tested. I have seen batteries right out of the box that were bad. You might not have enough cranking amps.
Kicking back is common if the battery is weak. Another reason of kickback is the motor is to far advanced, so you need to check the timing after you get it running.
Tyhe speedo cable screws into the speedo drive unit at the wheel. The square cable just slides in and then you turn the cable. It might be broken so the cable would have to be replaced or the drive unit is bad and it needs replaced. To replace or tighten the cable you have to loosen the end connected to the speedo.
The shifting problem might be a bent or worn shifter fork. the tranny would have to be pulled and inspected to see what the problem is.
Lastly, you sound like you have to chain the runs in the oil bath. There is oil in that cover. You can drain it and refill it about every 5000 miles.
Good luck and happy riding
Mike